The community-based structure of communication on social networking sites has long been a focus of scholarly attention. However, the problem of discovery and description of hidden communities, including defining the proper level of user aggregation, remains an important problem not yet resolved. Studies of online communities have clear social implications, as they allow for assessment of preference-based user grouping and the detection of socially hazardous groups. The aim of this study is to comparatively assess the algorithms that effectively analyze large user networks and extract hidden user communities from them. The results we have obtained show the most suitable algorithms for Twitter datasets of different volumes (dozen thousands, hundred thousands, and millions of tweets). We show that the Infomap and Leiden algorithms provide for the best results overall, and we advise testing a combination of these algorithms for detecting discursive communities based on user traits or views. We also show that the generalized K-means algorithm does not apply to big datasets, while a range of other algorithms tend to prioritize the detection of just one big community instead of many that would mirror the reality better. For isolating overlapping communities, the GANXiS algorithm should be used, while OSLOM is not advised.